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Abstract
The spectral radiance measurement at daytime level can be realized with high accuracy, while it’s difficult when the spectral radiance is at nighttime level. We design a spectral radiance calibration facility which has the characteristics of completely unchanged spectrum over 3 orders of magnitude and approximately unchanged spectrum for about 6 orders of magnitude. It combines a spectral radiance light source, a precision aperture and a white diffuser together, make it easy to reproduce the spectral radiance at 380 nm from 4 × 10−9 W/(m2·sr·nm) to 4 × 10−3 W/(m2·sr·nm). The facility can be easily used to calibrate a spectroradiometer at nighttime level. When the spectral radiance from 380 nm to 780 nm is around 1 × 10−7W/(m2·sr·nm), the calibration uncertainty of the spectroradiometer is 0.87%∼1.0% (k = 1).
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1. Introduction
The application of nighttime light images has become increasingly widespread in the past few decades. Nighttime light remote sensing can provide strong meteorological data and forest fire monitoring support. In addition, nighttime light remote sensing can effectively reflect the spatial distribution of human activities, such as the urbanization process, the regional economic growth, ecological light pollution, disaster monitoring and violent conflicts [1]. Different from the daytime scene, most of the visible and near-infrared light emitted from the surface at night is anthropogenic. The first earth observation during night is originated from the Defense Meteorological Satellite Program (DMSP). A photomultiplier tube was used to acquire signals at night in the initial stage [1]. In the 1970s, the Operational Linescan System (OLS) on the DMSP satellite acquired nighttime light images for the first time [2]. In 2011, the Suomi National Polar-orbiting Partnership (NPP) satellite was successfully launched. The Visible Infrared Imaging Radiometer Suite (VIIRS) sensor of Suomi NPP included a day-night band (DNB) which has the unique ability to make observation from daytime to very dim nighttime [3,4]. As a commercial satellite, the night images acquired by EROS-B could provide a much higher spatial resolution than DMSP-OLS [5]. For the International Space Station (ISS), nighttime measurements could not only be collected by dedicated instruments, but also be collected by the astronauts in the ISS [6]. In 2017 and 2018, China launched the JL1-3B and Luojia 1-01 satellites, which were mainly used for nighttime remote sensing [7,8]. In 2021, a civilian early-morning-orbit meteorological satellite FY-3E was launched. It carried a Medium Resolution Spectral Image-Low Light (MERSI-LL) sensor, which could image the earth from daytime to twilight [9].
At noon, the average spectral radiance of the land surface from 0.4 µm-1.1 µm is roughly 10−2 W/(cm2·sr·µm) [10]. While at night, the spectral radiation due to a full moon is nearly 500,000 times fainter than that due to the sun. When the land surface is illuminated by a new moon, the spectral radiance is around 10−10 W/(cm2·sr·µm), even 100 times fainter [3]. Nighttime remote sensing has made a big demand on the low light level detection capability of the satellite sensors. The reported lowest detectable radiance of DMSP-OLS is about 10−10 W/(cm2·sr·µm) [2]. The VIIRS DNB has a designed dynamic range from 3 × 10−9 to 10−2 W/(cm2·sr), covering 7 orders of magnitude [11]. The signal to noise is no less than 9 at the 3 × 10−9 W/(cm2·sr), enabling to image a illumination scene with the radiance around 10−10 W/(cm2·sr) [12–13]. The designed minimum detectable radiance of FY-3E MERSI-LL is 3 × 10−9 W/(cm2·sr) [9]. For all the satellite sensors, accurate calibration of instruments under low light levels is a key technical issue. Integrating sphere light sources are usually used for radiance calibration in the laboratory. A lamp can be encapsulated in a chamber or a small integrating sphere, connecting the main integrating sphere through a variable aperture. By adjusting the diameter of the aperture, the light flux entering the main integrating sphere can be controlled to change the spectral radiance level of the light source. F B Sadler reported a facility for optical calibration at low light level (FOCAL3), which has a full dynamic range of nearly 6 orders of magnitude [14]. Li introduced a low light level camera calibration facility, which can cover the range from 1 × 10−9W/(cm2·sr) to 3 × 10−2 W/(cm2·sr), with the uncertainty achieves 18%(k = 2) at the level of 10−9W/(cm2·sr) [15].
For most reports, radiance is used instead of spectral radiance. Since the radiation of the surface contains spectral information, the demand for low light level measurement has extended from initially panchromatic to multispectral. However, experiments show that the relative spectral distribution of the integrating sphere light source at different levels is not constant [16]. If a silicon detector is mounted on the integrating sphere to monitor the output level of the integrating sphere light source, the change of radiance is not equal to the change of spectral radiance. The spectral radiance can’t be evaluated accurately based on the monitor detector. If the spectral changes of the integrating sphere light source can’t be accurately characterized at different levels, there will be spectral mismatch when the satellite instruments are calibrated. Therefore, a calibration facility which can cover a large dynamic range with unchanged spectrum is desirable. However, there is a lack of reports on spectral calibration capability at low light level. J LaVeigne adopted a method to adjust the current of the integrating sphere light source to compensate for the spectral changes [17]. Wu used another integrating sphere and baffles to reduce the spectral variation [16]. In order to obtain a light source with nearly unchanged spectrum, a facility which can calibrate the spectroradiometer at low light level is developed.
2. Experimental methods
Figure 1 shows the spectral radiance calibration facility. The facility is placed on a 4 m by 1 m optical table. It consists of an integrating sphere light source, a black painted tube, an aperture, and a pressed polytetrafluoroethylene (PTFE) white diffuser. The integrating sphere light source, the tube and the aperture are all fixed on the optical table, while the white diffuser is mounted on a linear rail of the optical table. The normal direction of the exit plane of integrating sphere light source is parallel to the rail. The center of exit plane of the integrating sphere light source, the axis of the tube, the aperture and the white diffuser are collinear. The tube is used to limit the solid angle of the radiation from the integrating sphere light source to reduce the stray light. The outer diameter of the tube is 61 mm, and the clear aperture of the tube is 50 mm. The length of the tube is 110 mm. One side of the tube is closely attached to the exit plane of integrating sphere light source, while the other side is closely attached to the aperture plane. The combination of the integrating sphere light source, the tube and the aperture is called ISTA for short. The light radiation from ISTA can only be emitted from the aperture. The aperture can be fabricated with different inner diameters, but with the same outer diameter. The outer diameter is 70 mm, a little larger than that of the tube. The radiation emitting from the aperture is finally incident upon the white diffuser. Several baffles are mounted between the aperture and the white diffuser to minimize the effect of the stray light. Also, the surroundings of the facility are all covered with black aluminum foil BKF12 from Thorlabs to reduce the scattered stray light. A spectroradiometer is aiming at the center of the whiter diffuser to measure the reflected spectral radiance from the white diffuser. The angle θ between the normal direction of the white diffuser and the axis of the spectroradiometer is 45°. As the white diffuser slides on the rail, the distance between the aperture and the white diffuser can vary from 20 cm to 300 cm. Meanwhile, a baffle is used to block the radiation from ISTA to avoid exposure when not measured. In addition, the position of the spectroradiometer also needs to be adjusted as the distance changes.
Figure 2 shows the geometrical configuration of the optical setup. The aperture in front of the tube is located on the XYZ plane, while the white diffuser is located on the X1Y1Z plane. According to the propagation of fluxes of optical radiation, the spectral irradiance irradiated on the white diffuser and the spectral radiance measured by the spectroradiometer can be expressed by Eq. (1)–(4).
During the experiment, the distance between the front surface of the spectroradiometer and the center of the white diffuser is keeping at 400 mm. Considering that the field of view (FOV) of the spectroradiometer is 0.1°, it’s easy to calculate that the radius of the target is about 0.35 mm. If the diameter of the aperture is 20 mm and the distance is 20 cm, numerical calculation shows that the spectral irradiance difference between the center point and the region 0.35 mm away from the center is less than 0.01%. The target area of the spectroradiometer can be seen as a point, in other words x1 and y1 coordinates can be approximated as 0. On the other hand, numerical calculation shows that the difference between the average of the aperture and the center of the aperture is less than 0.25%. If the diameter of the aperture is decreased and the distance is increased, the target of the spectroradiometer and the aperture are more like a point. The spectral irradiance irradiated on the white diffuser approximately follows the inverse square law. If the diameter of the aperture is decreased from 20 mm to 6 mm and the distance is increased from 20 cm to 300 cm, the variation of the spectral irradiance can reach 2250 times. In ideal condition, the variation of the distance and the aperture size has no effect on the relative spectral distribution. On the other hand, the reflectance factor of an ideal white diffuser is close to 1. Therefore, the relative spectrum reflected from the white diffuser is extremely similar to the spectrum from the aperture of ISTA. When the diameter of the aperture is 6 mm and the distance is 300 cm, the spectral radiance reflected from the white diffuser is one millionth of the spectral radiance of ISTA. Therefore, a light source with the spectrum nearly unchanged while the dynamic range is about 1 million times can be realized. As a comparison, the length of the lab needs to be 200 m long if the variation of 1 million times is achieved only by changing the distance. Furthermore, if a second white diffuser is placed at the position of the spectroradiometer and the spectroradiometer is aiming at the center of the second white diffuser, the dynamic range will be much larger.
3. Results and discussion
The primary goal of the facility is to realize the spectral radiance at low light level and calibrate the responsivity of the spectroradiometer at different radiation levels. In the experiment, the spectroradiometer to be calibrated is a commercial one - Konica Minolta’s CS2000A, which can measure the spectrum between 380 nm and 780 nm. When the spectroradiometer is used to measure the spectral radiance at different levels, the measurement time will be different. The maximum measurement time can be as long as 240 s when the spectral radiance is decreased to 10−9 W/(m2·nm·sr). The integrating sphere light source - Gooch & Housego’s OL 455 is composed of a lamp chamber and an integrating sphere. The spectral radiance level can be adjusted by a micro-meter controlled variable aperture between the lamp and the entrance port of the integrating sphere. A silicon detector is mounted on the integrating sphere light source to monitor the stability and correct the drift during the experiment. When the integrating sphere light source is preheated for more than an hour, the stability is better than 0.15% in 1.5 hours.
Figure 3 shows the traceability chain of the low light level spectral radiance. First, the spectral radiance is traced back to a national primary standard of spectral radiance and spectral irradiance in China. The light source of the national primary standard is a high-temperature blackbody BB3500 M. The spectral radiance of the blackbody can be calculated using the Planck formula. A water-cooling aperture is mounted in front of the blackbody and a white diffuser is used to receive the spectral radiation from the blackbody. Then the facility composed of the blackbody, the water-cooling aperture and the white diffuser is used to calibrate the spectroradiometer. Next, the spectral radiance of ISTA is adjusted to a similar level which is generated by the blackbody, the water-cooling aperture and the white diffuser. Then the calibrated spectroradiometer is used to measure the spectral radiance of ISTA. When the spectral radiance of ISTA is obtained, the target spectral radiance can be realized using the low light level calibration facility. The spectral radiance transfer process from the blackbody to ISTA is similar to the 250 nm to 2500 nm spectral radiance or spectral irradiance realization process using the blackbody, which has already been published in previous papers [20,21]. Here we only focus on the realization of the low light level spectral radiance.
During the measurement, two different apertures with the diameter of 20.081 mm and 6.035 mm are used. The spectral radiance using the larger aperture is first measured at five different distances. The distance between the aperture and the white diffuser is set to 20 cm, 30 cm, 50 cm, 100 cm and 300 cm respectively. Finally, the spectral radiance using the smaller aperture is measured when the distance is 300 cm. It should be noticed that the variation of the spectral radiance related to the sun between 380 nm and 780 nm is less than 4 times, while the variation of ISTA is more than 40 times. Table 1 lists the spectral radiance at 380 nm, 500 nm and 780 nm when the measurement condition is varied. The spectral radiance values of ISTA are measured and transferred from the blackbody, while the other spectral radiance values are numerical calculation results according to the diameter and distance. It can be seen that when the distance is 300 cm and 6.035 mm aperture is used, the spectral radiance is nearly 1 millionth of ISTA.
Table 1. The spectral radiance at different levels
Figure 4 shows the radiance difference and the spectral radiance difference between numerical calculation and measurement results. The radiance is the integral of spectral radiance from 380 nm to 780 nm. The maximum deviation from the calculation is less than 0.70% and the average of the difference is less than 0.25%. Considering than the measurement accuracy is influenced by the stability, the length, the repeatability, the stray light and other influencing factors, the measurement results are consistent with the numerical calculations. For the spectral radiance, the difference shows obvious spectral characteristics. From 380 nm to 390 nm, the deviation is over 8.0% when the 20.081 mm aperture is used and the distance is 20 cm. And the deviation increases to 15% when the 20.081 mm aperture is used and the distance is 300 cm. It’s very likely that the responsivity of the spectroradiometer near 380 nm is not linear and the nonlinearity at different radiation levels should be corrected. From 400 nm to 780 nm, almost all the deviation is between -1.5% and 1.0%. As can be seen from the figure, the trend of the deviation fluctuation is very similar for all the six conditions. If the deviation difference between different conditions is calculated, the spectral characteristics can be significantly reduced. It is mainly due to the fact that the difference between six conditions only relates to the length and aperture variation. On the other hand, the spectral deviation shows obvious peaks in (545-585) nm and (720-760) nm region. It may be related to the accuracy of the spectral reflectance factor measurement of the white diffuser. When the 6.035 mm aperture is used and the distance is 300 cm, the spectral radiance difference shows clearly fluctuation from 400 nm to 450 nm. Since the spectral radiance at 400 nm is less than 8 × 10−9 W/(m2·sr·nm), the signal-to-noise ratio is significantly worse than the other conditions.
Fig. 4. The difference between numerical calculation and measurement results. (A) the radiance (B) the spectral radiance
The characterization of the facility and evaluation of the uncertainty is necessary when calibrating a spectroradiometer. The uncertainty is mainly related to three components in Eq. (1) and Eq. (2): the spectral radiance uniformity of the exit plane, the reflectance factor of the white diffuser, and the length. Since the uncertainty of length can be easily obtained, the uncertainty due to length will not be discussed here. Meanwhile, apertures with two different sizes are used, the influence due to the aperture size is also investigated.
3.1 Uniformity of the light source
If the spectral radiance at the aperture plane is not spatially uniform, correction is required in numerical calculation. It’s necessary to measure the surface uniformity of the aperture and evaluate the contribution. The spectroradiometer is equipped on a two-dimensional translation stage to scan the uniformity. During the surface uniformity scan, the axis of the spectroradiometer is at normal incidence to the aperture. First, the spectroradiometer aims at the top of the aperture. If x-axis and y-axis are used to describe the horizontal direction and the vertical direction, the coordinate of the highest aiming point in vertical direction is (0, 9.6) to ensure that the aiming area is entirely within the aperture. Then the spectroradiometer moves to the left side and right side respectively. When the 20.081 mm aperture is scanned, the movement interval is set to 2 mm except the outmost edge. The coordinates of the leftmost and rightmost points are (-9.6, 9.6) and (9.6, 9.6). After finishing the horizontal direction measurements, the spectroradiometer moves to (0, 8) and the scan is repeated. The movement interval in the vertical direction is the same as that in the horizontal direction. When the 6.035 mm aperture is scanned, the movement interval is set to 1 mm. The integral of the spectral radiance from 380 nm to 780 nm is used to describe the uniformity. Figure 5 shows the radiance uniformity on the aperture plane. It can be seen that the non-uniformity is less than 0.37% and 0.29% for the 20.081 mm and 6.035 mm aperture respectively. When the aiming points are at the edge of the aperture, the radiance is slightly smaller than the center point. It may be related to the size of source effect, which means part of the radiation beyond the target is received by the spectroradiometer [18]. On the other hand, the position with the highest value is not the center point for both aperture scans. Meanwhile, the spatial uniformity is a little different for the two apertures. It is possible that the integrating sphere light source is not an ideal centrosymmetrical light source. Also, the stability of the facility may affect the results since the scan of the large aperture takes much more time.
3.2 Spectral influence due to the aperture change
When the aperture of ISTA is changed, experiments show that the integral of spectral radiance from 380 nm to 780 nm of the 20.081 mm and 6.035 mm apertures are 33.42 and 33.41 W/(m2·sr) respectively. The integral difference is about 0.03% and can be nearly neglected. However, the spectral radiance changes slightly and should be corrected. Figure 6 shows the spectral radiance differences between the two apertures. The difference shows wavelength dependent characteristics. Due to the signal to noise ratio, the data exhibits obvious fluctuation, especially from 380 nm to 430 nm. From 540 nm to 700 nm, the difference is within ±0.06% and the average difference is less than 0.015%. On both sides of the spectrum, the maximum difference is around 0.20% and the average difference is less than 0.10%. The difference in both sides may be related to two reasons. First, when the diameter of the aperture is decreased, the light may be harder to escape from ISTA. Strictly speaking, the structure of ISTA is changed and there may be some changes in the internal reflection characteristics. If the diameter is decreased from 20 mm to 1 mm or even smaller, the spectral difference may be much larger. Second, the materials of the two apertures are not exactly the same, and the reflectivity of the back of the two apertures may have difference. If the light reflected from the back of the aperture entering the integrating sphere light source, the spectral distribution may be affected.
3.3 Reflectance factor of the white diffuser
The diffuse reflectance factor of the white diffuser under the geometric condition of 0:45 is measured using a multi-angle diffuse reflectance setup [19]. The reflectance factor from 380 nm to 780 nm is nearly the same and the maximum difference is less than 0.8%. The uncertainty of the reflectance factor is 0.50% from 380 nm to 780 nm. In principle, the angle θ in Fig. 1 should be fixed when the white diffuser and the spectroradiometer are moved. Due to the room limitation, the spectroradiometer can’t be mounted on a variable angle facility with its center aiming at the center of the white diffuser. During the measurement, there may be an angle positioning uncertainty. In order to evaluate the influence due to the angle error, the reflectance factor of the white diffuser needs to be measured at different angles. Due to the fact that the reflectance factor varies with angle and the trend of the variation is not related to wavelength, the average reflectance factor from 380 nm to 780 nm is used to describe the effect of angle. Figure 7 shows the average reflectance factor ratio as a function of angle θ using the multi-angle diffuse reflectance setup. The ratio is normalized using the data when θ equals 45°. Although the white diffuser is a good Lambertian, the reflectance factor of the white diffuser is not constant. As can be seen from the figure, the reflectance ratio shows approximately linear changes when the angle changes. When the angle θ increases 1 degree, the reflectance factor decreases by about 0.20%.
3.4 Uncertainty evaluation
In addition to the above influence factors, the calibration of the spectroradiometer also includes the stability of the light source, the aperture area, the repeatability of the spectroradiometer, the length measurement and the stray light. For a full moon night, the spectral radiance of land surface due to the moon is at the level of 1 × 10−7 W/(m2·sr·nm). In order to make the minimum spectral radiance at 780 nm reaches 1 × 10−7 W/(m2·sr·nm), the integrating sphere light source is decreased to approximately half of the previous level when the measurements in Table 1 is finished. The spectral radiance of the newly adjusted ISTA and the corresponding spectral radiance when the distance is 300 cm and the diameter of the aperture is 6.035 mm, are then measured.
The uncertainty at a full moon level is evaluated and the uncertainty components are listed in Table 2. The combined standard uncertainty is no more than 1.0% when the spectral radiance of every wavelength is around 1 × 10−7 W/(m2·sr·nm). The facility can provide a low light level calibration with high accuracy. Furthermore, the facility can be used to realize spectral radiance at the level of 10−9 W/(m2·sr·nm). For the minimum radiation level in Fig. 4, the spectral radiance of 380 nm and 400 nm is 4.47 × 10−9 W/(m2·sr·nm) and 7.96 × 10−9 W/(m2·sr·nm) respectively. In principle, if the performance of the spectroradiometer is excellent, the facility can provide a similar calibration uncertainty even at such a low spectral radiance level. However, the relative standard deviation of 10 measurements at 380 nm and 400 nm is 17% and 3.4% respectively. It’s obvious that the uncertainty due to repeatability is the largest component and the calibration uncertainty is totally determined by the repeatability of the spectroradiometer. When the radiation level of ISTA is decreased further, the calibration of the spectroradiometer will be almost independent of the performance of the facility, but dependent on the measurement capability of the spectroradiometer.
Table 2. Uncertainty of the calibration of the spectroradiometer at full moon level
4. Conclusion
We have proposed a low light level spectral radiance realization method which is predictable based on the fundamental property of optical radiation. The method can make the dynamic range of the light source reaching 1 million times, while the spectrum remains approximately unchanged. By tracing back to the high temperature blackbody, the dissemination chain of spectral radiance at low light level is also given. In the experiment, the spectral radiance at 380 nm can be varied from 4.392 × 10−3 W/(m2·sr·nm) to 4.470 × 10−9 W/(m2·sr·nm), while the spectral radiance at 780 nm can be varied from 1.836 × 10−1 W/(m2·sr·nm) to 1.883 × 10−7 W/(m2·sr·nm). In addition, the low light level spectral radiance calibration facility can be used to support the responsivity calibration of spectroradiometer covering nearly 6 orders of magnitudes. In fact, the reflectance factor of the white diffuser is nearly flat from 380 nm to 1500 nm or even longer wavelength, the facility is suitable to calibrate the linearity of the spectroradiometer with a much longer wavelength range. Assuming the spectral radiance of ISTA is L0(λ), the spectroradiometer can be calibrated at a spectral radiance level of 10−6 L0(λ). If the signal to noise of the spectroradiometer is good enough, the calibrated spectroradiometer can be used to calibrate a new ISTA at 10−6L0(λ) level with high accuracy. And, if the influence of the background environment of the facility can be effectively limited to a near ideal condition, the method can be iteratively used and the facility can further extend the spectral radiance to even lower level.
Funding
National Key Research and Development Program of China (2022YFF0610802); National Institute of Metrology, China (AKYZD2210).
Acknowledgments
The authors thank Xiaofeng Lu for helpful discussion.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the corresponding author upon reasonable request.
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